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JEE Main20203 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

The function, f x = 3 x - 7 x 2 3 , x ∈ R , is increasing for all x lying in

Options

  1. A- ∞ , 0 ∪ 14 15 , ∞
  2. B- ∞ , 0 ∪ 3 7 , ∞
  3. C- ∞ , 14 15
  4. D- ∞ , - 14 15 ∪ 0 , ∞

Correct answer

A. - ∞ , 0 ∪ 14 15 , ∞

Step-by-step solution

f x = 3 x - 7 x 2 3 For f x is increasing f ' x > 0 . Differentiate f x f ' x = 3 x 2 3 + 3 x - 7 2 3 x 1 3 f ' x = 9 x + 2 3 x - 7 3 x 1 3 f ' x = 15 x - 14 3 x 1 3 Now f ' x > 0     ⇒ 15 x - 14 3 x 1 3 > 0 x ∈ - ∞ ,   0 ∪ 14 15 ,   ∞

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